Inverse problems for linear hyperbolic equations using mixed formulations

We introduce in this document a direct method allowing to solve numerically inverse type problems for linear hyperbolic equations. We first consider the reconstruction of the full solution of the wave equation posed in $\Omega\times (0,T)$ - $\Omega$ a bounded subset of $\mathbb{R}^N$ - from a partial distributed observation. We employ a least-squares technique and minimize the $L^2$-norm of the distance from the observation to any solution. Taking the hyperbolic equation as the main constraint of the problem, the optimality conditions are reduced to a mixed formulation involving both the state to reconstruct and a Lagrange multiplier. Under usual geometric optic conditions, we show the well-posedness of this mixed formulation (in particular the inf-sup condition) and then introduce a numerical approximation based on space-time finite elements discretization. We prove the strong convergence of the approximation and then discussed several examples for $N=1$ and $N=2$. The problem of the reconstruction of both the state and the source term is also addressed

PUBLIC – PRIVATE PARTNERSHIP IN PROVIDING PUBLIC GOODS AND SERVICES

Local administrations are searching for new ways to efficiently deliver services and to develop and maintain the infrastructure that allows economic development. Increasingly, they are turning to public-private partnerships to do so. PPPs covers a wide range of partnerships arrangements, such as: outsourcing, joint ventures, concessions, sales of equity stakes in state owned business, privatization, private finance initiative, but these forms of PPPs are not adopted by all specialists. Some organizations and specialists exclude privatization from the PPPs, because in their opinion PPPs are viable alternatives to privatization. The concept of PPP is very ambiguous.public-private partnership, concession, outsourcing, privatization

Impact on the fate of the euro area economy

Regarding the impact of EMU on euro area firms' competitiveness and their capacity to play an important role in international markets, recent research indicates Euro contribution to increasing the competitiveness of firms by facilitating trade between countries in the eurozone and by promoting the single market integration EU. Euro zone countries are considered to be the best export base, attracting a larger number of companies from neighboring countries. Euro area enlargement and better integrate it, in addition to allowing firms to diversify their operations to lower marginal costs, also tend to be more closely associated with competition and thus a higher variety of products, higher productivity and lower pricescompetitiveness, financial integration, market integration, foreign direct investment

A mixed formulation for the direct approximation of the control of minimal L2L^2-norm for linear type wave equations

This paper deals with the numerical computation of null controls for the wave equation with a potential. The goal is to compute approximations of controls that drive the solution from a prescribed initial state to zero at a large enough controllability time. In [\textit{Cindea, Fernandez-Cara \& Münch, Numerical controllability of the wave equation through primal methods and Carleman estimates, 2013}], a so called primal method is described leading to a strongly convergent approximation of boundary controls : the controls minimize quadratic weighted functionals involving both the control and the state and are obtained by solving the corresponding optimality condition. In this work, we adapt the method to approximate the control of minimal square-integrable norm. The optimality conditions of the problem are reformulated as a mixed formulation involving both the state and his adjoint. We prove the well-posedeness of the mixed formulation (in particular the inf-sup condition) then discuss several numerical experiments. The approach covers both the boundary and the inner controllability. For simplicity, we present the approach in the one dimensional case

Controllability of the linear 1D-wave equation with inner moving forces

This paper deals with the numerical computation of distributed null controls for the 1D wave equation. We consider supports of the controls that may vary with respect to the time variable. The goal is to compute approximations of such controls that drive the solution from a prescribed initial state to zero at a large enough controllability time. Assuming a geometric optic condition on the support of the controls, we first prove a generalized observability inequality for the homogeneous wave equation. We then introduce and prove the well-posedness of a mixed formulation that characterizes the controls of minimal square-integrable norm. Such mixed formulation, introduced in [\textit{Cindea and Münch, A mixed formulation for the direct approximation of the control of minimal ${L}^2$-norm for linear type wave equations}], and solved in the framework of the (space-time) finite element method, is particularly well-adapted to address the case of time dependent support. Several numerical experiments are discussed

Approximation of periodic solutions for a dissipative hyperbolic equation

This paper studies the numerical approximation of periodic solutions for an exponentially stable linear hyperbolic equation in the presence of a periodic external force $f$. These approximations are obtained by combining a fixed point algorithm with the Galerkin method. It is known that the energy of the usual discrete models does not decay uniformly with respect to the mesh size. Our aim is to analyze this phenomenon's consequences on the convergence of the approximation method and its error estimates. We prove that, under appropriate regularity assumptions on $f$, the approximation method is always convergent. However, our error estimates show that the convergence's properties are improved if a numerically vanishing viscosity is added to the system. The same is true if the nonhomogeneous term $f$ is monochromatic. To illustrate our theoretical results we present several numerical simulations with finite element approximations of the wave equation in one or two dimensional domains and with different forcing terms

ONLINE ADVERTISING – A PRACTICAL APPROACH USING GOOGLE’S AD WORDS

The Internet links people from all around the world in their purpose to exchange and get relevant information. Thus, relevant information is the corner stone of a society in general and of a company in particular. The exchange process within the information era is been initiated and controlled by the client. The marketers must wait until the clients decide to participate in the exchange. The clients define what information they need, what offers they are interested in and what prices they are willing to pay. This development enabled companies like Google to manage the different companies’ online targeted advertising using the initial query of the searching persons. Online advertising is nowadays an essential component of one’s company’s promotional mix.SEM (Search engine marketing), online advertising, CPC (cost per click), CTR (click-through rate), Ad Words, Ad Group

Bedeutung der 68Ga-DOTATATE PET/CT in der Primär- und Rezidivdiagnostik neuroendokriner Tumoren

Neuroendokrine Tumoren sind eine Entität heterogener Neoplasien, welche sich von neuroendokrinen Zellen herleiten. Ihre Inzidenz in der Allgemeinbevölkerung ist mit etwa 1:100.000 gering, und das obwohl sie innerhalb der letzten Jahrzehnte durch verbesserte Diagnostik und ein verstärktes Bewusstsein zugenommen hat. Die verbesserte Diagnostik bedeutet eine Vielfalt von Möglichkeiten in der Bildgebung. Es gilt, diese Möglichkeiten auf ihre diagnostischen Fähigkeiten hin zu untersuchen. Ziel dieser Arbeit war es, aus dem Patientengut der nuklearmedizinischen Kliniken der LMU Großhadern und Innenstadt die diagnostischen Fähigkeiten des Tracers 68Ga – DOTATATE für die Primär – und Rezidivdiagnostik neuroendokriner Tumoren retrospektiv zu evaluieren. 173 Patienten, welche zwischen den Jahren 2006 und 2011 in mindestens einer der beiden Kliniken eine 68Ga – DOTATATE PET/CT – Untersuchung erhalten haben, wurden ausgewählt. 104 Patienten stellten sich wegen Verdacht auf einen neuroendokrinen Tumor vor, bei 69 wurde ein Rezidiv eines neuroendokrinen Tumors vermutet. Alle Vor – und Nachuntersuchungen der Patienten wurden genau analysiert, histologische Befunde wurden berücksichtigt und im Zweifelsfall oder zum Follow – up wurde der jeweilige Hausarzt oder der Patient selbst kontaktiert. Falls vorhanden, wurden die Werte für Chromogranin A und NSE erfasst und ausgewertet. In Zusammenschau aller Ergebnisse zeigt der Tracer 68Ga – DOTATATE in der Primärdiagnostik eine Sensitivität von 80% und eine Spezifität von 88,4%. Der Positiv Prädiktive Wert ist 77,8% und der Negativ Prädiktive Wert 89,7%. Für die Rezidivdiagnostik gelten folgende Zahlen: Sensitivität = 89,7%, Spezifität = 80,0%, PPW = 76,5%, NPW = 91,4%. Die Werte für Chromogranin A waren in der Primärdiagnostik und im Gesamtkollektiv in der Gruppe der NET – Patienten signifikant erhöht (PD: 2087,14 ng/ml vs. 315,95 ng/ml, p<0,05; G: 1410,29 ng/ml vs. 289,10 ng/ml, p<0,05). In der Primärdiagnostik und im Gesamtkollektiv waren in der Gruppe der PET – positiven Patienten die Mittelwerte für Chromogranin A zwar deutlich, aber nicht signifikant verschieden (PD: 1898,85 ng/ml vs. 517,44 ng/ml, p<0,2; G: 1404,87 ng/ml vs. 240,54 ng/ml, p<0,1). In der Rezidivdiagnostik unterschieden sich weder die NET – noch die PET – Gruppen wesentlich bezüglich der Chromogranin A - Werte. Die Mittelwerte für NSE waren in allen Gruppen (bis auf RD PET) signifikant verschieden. Mithilfe präexistenter Literatur bezüglich bildgebender Verfahren für neuroendokrine Tumoren allgemein sowie anderer Positronen – emittierender Tracer wurde die Bedeutung des 68Ga – DOTATATE für NET in der Nuklearmedizin eingeschätzt. Zusammenfassend kann man sagen, dass 68Ga – DOTATATE eine hohe Treffsicherheit in der Entdeckung von neuroendokrinen Tumoren und ihren Rezidiven besitzt und somit einen wichtigen Stellenwert im klinischen Alltag einnimmt

Pelayanan Berbasis Digital: Implementasi Aplikasi Pendaftaran Antrian Paspor Online (APAPO) di Kantor Imigrasi Tanjungpinang

This The development of this information technology is utilized by the Immigration Class 1 TPI Tanjungpinang to improve services by making it easier for people to register for passport applications with the support of the Online Passport Queue Registration Application (APAPO) which has been used since January 2019. The application of this Online Passport Service is a form of service improvement carried out by the Tanjungpinang City Immigration Office to handle public complaints regarding the queue for passport processing. Online passport services can be downloaded via smartphones in the Playstore and Appstore. At the Immigration Office Class 1 TPI Tanjungpinang there is information on a stop extortion poster, but the reality is that extortion is still being carried out by civil servants at the passport application service. This research was conducted using qualitative research methods. This method is used in the process of data acquisition and data analysis process. The qualitative method used tends to be descriptive in terms of obtaining and analyzing money data. Implementation is a plan that has been conceptualized in carrying out a clear goal. Implementation itself certainly has a goal, the purpose of an implementation is to realize a plan that has been structured that can be implemented properly. The online passport queue application is a new output issued by the government in carrying out digital-based innovations that can be carried out by the community and make it easier for the community